A man goes to the fair in Funcity with his son and faithful dog. Unfortunately man misses his son which he realises 20 minutes later. The son comes back towards his home at the speed of 20 m/min and man follows him at 40 m/min. The dog runs to the son(child) and comes bac to the man(father) to show him the direction of his son. It keeps moving to and fro at 60 m/min between son and father, till the man meets the son. What is the distance travelled by the dog in the direction of the son?

Options

A. 800 m
B. 1675 m
C. 848 m
D. 1000 m

Answer

To solve the problem step by step, we will analyze the movements of the man, son, and dog, and calculate the distance traveled by the dog in the direction of the son.

### Step 1: Determine the time before the man realizes his son is missing.
The man realizes that his son is missing after 20 minutes.

**Hint:** Keep track of the time intervals in the problem as they are crucial for calculating distances.

### Step 2: Calculate the distance the son travels in 20 minutes.
The son walks back towards home at a speed of 20 m/min.
- Distance traveled by the son = Speed × Time = 20 m/min × 20 min = 400 meters.

**Hint:** Remember to use the formula for distance: Distance = Speed × Time.

### Step 3: Determine the relative speeds of the man and son.
The man follows his son at a speed of 40 m/min, while the son is moving back towards home at 20 m/min.
- The effective speed of the man relative to the son = Speed of the man - Speed of the son = 40 m/min - 20 m/min = 20 m/min.

**Hint:** When two objects move in the same direction, subtract their speeds to find the relative speed.

### Step 4: Calculate the time taken for the man to catch up to the son.
The son is 400 meters ahead when the man starts chasing him.
- Time taken to catch up = Distance / Relative Speed = 400 m / 20 m/min = 20 minutes.

**Hint:** Use the formula for time: Time = Distance / Speed.

### Step 5: Determine the total time the dog is running.
The dog runs back and forth between the man and the son until they meet. The dog starts running after 20 minutes, when the man realizes his son is missing, and continues until the man catches the son, which takes another 20 minutes.
- Total time the dog runs = 20 min (before the man realizes) + 20 min (while the man is chasing) = 20 minutes.

**Hint:** Make sure to account for the total time the dog is active in the problem.

### Step 6: Calculate the distance traveled by the dog.
The dog runs at a speed of 60 m/min.
- Distance traveled by the dog = Speed × Total Time = 60 m/min × 20 min = 1200 meters.

**Hint:** Again, use the distance formula: Distance = Speed × Time.

### Final Answer:
The distance traveled by the dog in the direction of the son is **1200 meters**.